Circunstancias de contexto
1. Causas del maltrato infantil
We have shown that an increase in the price of oil leads to stagflation as well as temporary balance of trade problems for oil-dependent economies, while the precise degree of severity of these effects depends upon the degree of oil-dependency and the currency in which OPEC oil is denominated. This section analyzes the consequences of various monetary policy reactions that could be employed by the domestic and foreign economy in an effort to reduce the potentially disruptive effects of oil price shocks. The section is organized as follows: We first consider monetary policy rules that are calculated to fix the growth rate of the consumer price index at its initial equilibrium level at all times. In a first step we discuss the problem of complete stabilization of the inflation rate based on the consumer price index over the time interval T < t < ∞. Since the anticipation of a future increase in the price of oil not only results in inflation after the realization of the materials price increase but also during the time span between the anticipation and the implementation of the oil price shock, we also analyze the problem of fixing the consumer price inflation ˙pc at its initial steady state level for all t > 0. In the second part of this section we analyze the problem of complete system stabilization: Is monetary policy able to neutralize all adjustment dynamics that result from an anticipated increase in the price of raw materials imports? The absorption of the dynamic effects of anticipated oil price shocks means fixing the endogenous variables of the world system at their respective initial steady state level during the whole anticipation phase and after the implementation of the oil price increase fixing them at their respective new steady state level for all t > T . We will show that this is possible by a suitable combination of contractionary domestic and foreign monetary policy but that there may occur time inconsistency problems.
6.1 Stabilization of the Consumer Inflation Rate
We first consider the problem of fixing the domestic consumer inflation rate ˙pc at its initial steady state level ˙pc = 0 for all t > T .46 Such an effect may be achieved by adjusting the growth rate of domestic money supply according to the policy rule
˙
m = (1 − α) ˙τ +1 2˙ls+1
2˙ld (32)
This rule must be credibly announced at time t = 0 to be implemented at the date of the oil price increase T . Since the rise of p∗R leads to temporary inflation (cf. figure 4) it is obvious that ˙m must be negative for T < t < ∞ (figure 16). The policy rule (32) not only prevents consumer price inflation for all t > T but also leads to a dampening of the price and wage inflation rates ˙p and ˙w (figure 17). Since the policy rule is anticipated by the public it leads to adjustment dynamics during the time span 0 < t < T (figure 18).
The contractionary monetary policy rule causes on impact a rise of the terms of trade τ , a decline in domestic output and deflation, i.e. a fall of the inflation rates ˙p and ˙pc during
46We assume that initially ˙m0= 0 holds.
the whole anticipation phase 0 < t < T .47 On the other hand, it leads to an increase of foreign output and to foreign inflation during the time span 0 < t < T .
To avoid domestic deflation during the anticipation period the monetary policy rule (32) must already be implemented at the time of anticipation of the oil price shock, i.e. at t = 0. It then guarantees ˙pc = 0 at any time t > 0. Note that the growth rate of money supply that is induced by the policy rule (32) must be positive for 0 < t < T (figure 19).
This is not surprising since the anticipation of a future contraction in monetary growth rate as a response to the realization of the oil price increase causes on impact domestic disinflation which can only be removed by an expansionary monetary policy over the time interval 0 < t < T .
A unilateral fixing of the rate of change of the domestic price index with the help of the domestic policy rule (32) has the drawback that it causes foreign inflation during the anticipation phase and is unable to reduce the inflationary effects for the foreign economy which occur after the implementation of the oil price increase (figure 20).
A simultaneous stabilization of the domestic and foreign consumer inflation rate at their respective initial steady state level is only possible if in addition to the domestic monetary policy rule an analogous foreign policy rule is implemented at the time of an-ticipation of the oil price shock:
˙
m∗ = −(1 − α∗) ˙τ +1 2˙ls− 1
2˙ld (33)
Figure 21 shows that the growth rate of foreign money supply that results from (33) is negative for both t < T and t > T . It must be negative for T < t < ∞ in order to eliminate foreign inflation for t > T . In contrast to domestic monetary policy it must also be negative during the anticipation phase 0 < t < T since the implementation of the domestic monetary policy rule leads to relatively strong foreign inflationary effects over the time interval 0 < t < T . These effects can not be neutralized by the anticipation effects of the contractionary foreign monetary policy rule (33) if it is implemented at time T .
47The fact that a credible announcement of a contractionary monetary policy leads to disinflation even before the contraction actually occurs is a well known result, see Ball (1994). Due to the contractionary effect of the real appreciation we do not find – in contrast to Ball (1994) in an closed economy model – a disinflationary boom in our open economy framework.
10 20 30 40
real factor prices
real interest rates
q
Figure 16: Development of domestic monetary growth rate ˙m according to the policy rule (32)
10 20 30 40
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
Figure 17: Response of domestic price and wage inflation rate ˙p and ˙w respectively to an unsta-bilized (solid lines) and a staunsta-bilized oil price shock (dashed lines)
0.2 0.4 0.6 0.8 1
real factor prices real interest ratesq q∗
real factor prices real interest rates
q
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest ratesq
q∗
real factor prices real interest ratesq q∗
Figure 18: Response of terms of trade τ , domestic output q, domestic price inflation rate ˙p, domestic consumer price inflation rate ˙pc, foreign output q and foreign consumer inflation rate
˙p∗c to an isolated oil price shock (solid lines) and to a stabilized oil price shock (dashed lines) during the anticipation period
0.2 0.4 0.6 0.8 1
real factor prices
real interest rates
q
Figure 19: Development of domestic monetary growth rate ˙m during the anticipation period according to the policy rule (32)
0.2 0.4 0.6 0.8 1
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
Figure 20: Response of foreign consumer inflation rate ˙p∗c to an unstabilized (solid lines) and a stabilized (dashed lines) oil price shock
0.2 0.4 0.6 0.8 1
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
Figure 21: Development of foreign monetary growth rate ˙m∗ according to the policy rule (33)
0.2 0.4 0.6 0.8 1
real factor prices real interest rates
q
real factor prices real interest rates
q
real factor prices real interest ratesq
q∗
real factor prices real interest ratesq
q∗
Figure 22: Response of domestic and foreign output q and q∗ respectively to an isolated oil price shock (solid lines) and to a stabilized oil price shock (dashed lines)
6.2 Complete System Stabilization
The implementation of the policy rules (32) and (33) has the disadvantage that during the time interval 0 < t < ∞ it leads to a permanent change of the growth rate of do-mestic and foreign money supply. A further disadvantage is that, with the exception of the inflation rates ˙pc and ˙p∗c, they cannot prevent adjustment dynamics of the endoge-nous variables induced by the oil price shock. In particular, the contractionary output effects after the realization of the oil price shock are temporarily increased (figure 22).
The question therefore arises whether monetary policy is able to eliminate all dynamic effects of an anticipated increase of the price of raw materials imports. On the one hand, that means the neutralization of the anticipation effects of a future rise of p∗R, i.e. the fixing of all endogenous variables of the system at their respective initial steady state level for 0 < t < T . On the other hand, complete system stabilization requires an instanta-neous jump into the new steady state of the whole system after the implementation of the materials price increase. In this case there are also no adjustment processes in the period after the exogenous price shock. If this is possible by a suitable monetary policy, adjustment dynamics (for example business cycles or divergent economic developments across the large open economies) can be avoided both for t < T and t > T . In the mathematical appendix it is shown that the economic policy goal of complete system sta-bilization is attainable by an international coordination of monetary policy which requires a once-and-for-all reduction of both the domestic and foreign growth rate of money supply.
Dynamic Effects of an Oil Price Increase under Endogenous Oil Pricing Rules A permanent decline of the growth rate of foreign money supply (d ˙m∗ < 0) has the effect that – given a constant US dollar price of imported raw materials for t > T – no steady state of the foreign real factor price p∗R− p∗ exists. Without a permanent adjustment of the price of oil there would be a long run positive or negative growth of the real factor price p∗R− p∗ with the rate ˙p∗R− ˙p∗1 = − ˙m∗1 = −( ˙m∗0+ d ˙m∗).48 It seems therefore natural to endogenize the foreign-currency price of oil according to the pricing rule49
˙p∗R= ˙m∗ (34)
or
˙p∗R= ˙p∗ (35)
The pricing rule can be rationalized if the initial steady state is characterized by a positive growth rate of foreign money supply (i.e., ˙m∗0 > 0) so that the foreign inflation rate is initially positive ( ˙p∗0 = ˙m∗0> 0). Given a fixed level of the US dollar price of oil the foreign real factor price p∗R− p∗ would then fall continuously throughout the anticipation phase leading to a continuous deterioration of the terms of trade of the oil-exporting nation with
48Note that in the long run the inflation rate is determined by the growth rate of money supply. ˙m∗0 denotes the initial, ˙m∗1the new monetary growth rate. If ˙m∗0> 0 then ˙m∗1may also be positive although d ˙m∗< 0.
49It is also possible to couple ˙p∗R with − ˙e if oil imports are priced in dollars. Cf. Yousefi and Wirjanto (2004).
respect to the large foreign economy. To prevent such a process of real depreciation from the perspective of the oil-exporting economy the rate of change of the oil price must be coupled with the monetary growth rate ˙m∗ or the foreign inflation rate ˙p∗. In the first case both the adjustment dynamics and steady state effects of a once-and-for-all increase of the factor price p∗R remain unchanged while under the second materials pricing rule the dynamics and long run effects change considerably compared with the benchmark scenario ˙p∗R = ˙m∗ = 0.50 If the rate of change of the foreign-currency price of oil is coupled with the foreign inflation rate ˙p∗ then the real factor price p∗R− p∗ does not rise for 0 < t < T (as in the benchmark case) but persists at its initial steady state level during the whole anticipation phase. At the date of implementation of the oil price increase the real factor price p∗R− p∗ rises by the same amount as p∗R and remains at its new steady state level thereafter (figure 23). A further striking result that differs considerably from the benchmark scenario is the real appreciation of the domestic currency over the interval 0 < t < T causing a domestic output contraction on impact and a foreign output expansion (figure 25).
At the date of implementation of the oil price rise there is now a discontinuous increase of q and q∗ – although the real factor prices p∗R+ e − p and p∗R− p∗ rise sharply at time T (figure 23). The reason is that at time T a strong increase of the consumer inflation rates
˙pc and ˙p∗c takes place (figure 24) leading to a strong fall of the domestic and foreign real interest rate. After the output jump in T a sharp output contraction in both economies occurs (figure 25). Since the long run rise of the real factor prices is reinforced if ˙p∗R is coupled with the inflation rate ˙p∗, the steady state output contraction in both economies is stronger than in the benchmark scenario. From the perspective of the oil-exporting nation the steady state improvement of its terms of trade (i.e., the real factor prices) with respect to the oil-importing economies is reinforced (figure 23). According to equations (24) and (25) this does not imply that the real oil imports of the large open economies increase in the long run. On the contrary, the steady state rise of the domestic and foreign trade balance with respect to OPEC is generally increased under the pricing rule ˙p∗R= ˙p∗.
50Note that if ˙m∗> 0 initially and ˙p∗R= ˙m∗holds, the input price p∗R already increases continuously during the time interval 0 < t < T , i.e., before the discontinuous price shock dp∗R > 0 occurs. The same holds under the pricing rule ˙p∗R = ˙p∗, since ˙p∗ > 0 for 0 < t < T if ˙p∗R is coupled with ˙p∗. Note that in the benchmark scenario, i.e. in case ˙p∗R = ˙m∗ = 0, the foreign inflation rate is negative for 0 < t < T (cf.
figure 4). Under the pricing rule ˙p∗R= ˙p∗the development of the foreign inflation rate ˙p∗is identical with the adjustment of the wage rate ˙w∗, since in this case equation (14) is equivalent to ˙p∗= ˙w∗.
0.2 0.4 0.6 0.8 1
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗ to an anticipated oil price increase in the benchmark case (solid lines) and in the case ˙p∗R = ˙p∗ (dashed lines)
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
Figure 24: Response of domestic and foreign consumer price inflation rate ˙pcand ˙p∗c respectively to an anticipated oil price increase in the benchmark case (solid lines) and in the case ˙p∗R = ˙p∗ (dashed lines)
0.2 0.4 0.6 0.8 1
real factor prices real interest ratesq q∗
real factor prices real interest ratesq q∗
real factor prices real interest rates
q
real factor prices real interest rates
q
real factor prices real interest ratesq
q∗
real factor prices real interest ratesq
q∗
Figure 25: Response of terms of trade τ , domestic and foreign output q and q∗ respectively to an anticipated oil price increase in the benchmark case (solid lines) and in the case ˙p∗R= ˙p∗(dashed lines)
The System-Stabilizing Monetary Policy
Consider now the international coordination of monetary policy to attain complete system stabilization if either the materials pricing rule (34) or (35) holds. We first discuss full system stabilization in the period 0 < t < T prior to the implementation of the rise of the US dollar price of oil. In the mathematical appendix it is shown that the removal of any anticipation effects of a future oil price shock is achievable by the credible announcement of a unilateral monetary policy action at time t = 0 to take effect at the time of imple-mentation of the factor price increase. If the materials pricing rule ˙p∗R = ˙m∗ holds, the exogenous price shock dp∗R> 0 leads on impact to a fall of the domestic terms of trade τ (τ (0+) < τ0, cf. figure 2). Fixing τ at its initial steady state level τ0 requires the credible announcement of a contractionary domestic monetary policy, i.e. d ˙mann. < 0.51 In case of the pricing rule ˙p∗R= ˙p∗ the terms of trade τ rise on impact (cf. figure 25) so that the credible announcement of a contractionary foreign monetary policy (i.e., d ˙m∗ ann. < 0) stabilizes τ and the other endogenous variables at their respective initial steady state level during the whole anticipation phase.52. In particular, the inflation rates remain constant in this period and no output contraction can occur prior to the implementation of the oil price increase.
If the domestic and foreign central bank in the case of the pricing rule ˙p∗R= ˙m∗ and
˙p∗R = ˙p∗ respectively implement the announced reduction in monetary growth and given the discretionary increase of the oil price in T , the state vector (ls, τ, ld)0 continuously moves in period t > T to a new steady state that differs from that one in the case of a passive monetary policy. In a phase diagram the state vector (ls, τ, ld)0 without jump converges across a stable trajectory from its initial steady state towards its new steady state (figure 26).53 In comparison with the new steady state in case of a passive monetary policy we get the same rise of the equilibrium value of the terms of trade τ (cf. figure 27). On the other hand, the long run fall of the aggregate monetary state variable ls induced by the oil price increase dp∗R> 0 is now weaker, since the monetary policy d ˙m < 0 (d ˙m∗ < 0 in case
˙p∗R= ˙p∗ respectively) in isolation leads to a rise of the steady state variable ls. The same holds for the difference variable ldin case d ˙m < 0 (cf. figure 27, left), while the fall of ldis reinforced if d ˙m∗ < 0 holds (cf. figure 27, right).54 Adjustment dynamics throughout the
51The precise formula for d ˙mann. is given in the mathematical appendix, Section D. Note that the policy is consistent with the goal of price stability since it does not lead to a long run rise of the domestic inflation rates ˙p and ˙pc.
52It is a well known result that the anticipation of a future once-and-for-all fall of the growth rate of money supply leads on impact to a real appreciation. See, for example, Clausen and Wohltmann (2005).
53The trajectory lies on the stable saddle path belonging to the initial steady state. The formula for the stable saddle path, which is a hyperplane in the case of a three-dimensional state vector, is presented in the mathematical appendix.
54The corresponding multipliers are given by
∂ls
∂ ˙m = ∂ld
∂ ˙m = −l2
∂ls
∂ ˙m∗
¯¯
¯¯
˙ p∗R= ˙p∗
= − ∂ld
∂ ˙m∗
¯¯
¯¯
¯p˙∗R= ˙p∗
= −l2
period after the oil price shock also occur for the other endogenous variables of the system (cf. figure 28), i.e. cannot be avoided by the implementation of the announced restrictive monetary policy. Since the stabilization of the system prior to the implementation of the oil price shock requires a weak contractionary monetary policy the output development for t > T in the case of an active monetary policy differs only slightly from the corresponding output adjustment in case of a passive monetary policy (cf. figure 28). Compared with the case of a passive monetary policy (d ˙m = 0) the jumps of the inflation rates at time T are now slightly smaller (figure 29). Moreover, a long run fall of the domestic inflation rates takes place if d ˙mann.< 0 is actually implemented.55
The removal of any adjustment dynamics throughout the period t > T will only be achieved if the central bank deviates from the previously announced and therefore antici-pated contractionary monetary policy by implementing a reduction of the growth rate of money supply which is stronger than the announced one (i.e., d ˙mimpl. < d ˙mann.). More-over, full system stabilization for t > T is not attainable by a unilateral monetary policy response but requires a simultaneous coordinated action of the domestic and foreign cen-tral bank in the sense that both the domestic and foreign monetary growth rate must be reduced at time T in a non-anticipated manner (i.e., d ˙mimpl. < 0 and d ˙m∗ impl. < 0, cf.
figure 30).56 An analogous result holds in case d ˙m∗ ann.< 0, i.e. if the pricing rule ˙p∗R= ˙p∗ holds.
In the mathematical appendix it is shown that the realized domestic and foreign mon-etary policy does not depend upon the underlying materials pricing rule. It can also be shown that the long run total change of any endogenous variable remains unchanged if the pricing rule ˙p∗R= ˙m∗ is replaced by ˙p∗R= ˙p∗. In particular,
dx|p˙∗
R= ˙m∗ = dx|p˙∗
R= ˙p∗ for x ∈ {q, q∗} (36) holds. Since foreign monetary policy has long run output effects, if ˙p∗R = ˙m∗, while it is neutral under the pricing rule ˙p∗R = ˙p∗57, equation (36) implies that the decrease of ˙m∗ reinforces the long run output contraction of oil price shocks, provided ˙p∗R = ˙m∗ holds.
The total output contraction induced by the oil price shock and the monetary policy response coincides with the long run output decrease of the price shock in case p∗R= ˙p∗.58 The required reduction of ˙m and ˙m∗ to achieve full system stabilization is determined by
The total output contraction induced by the oil price shock and the monetary policy response coincides with the long run output decrease of the price shock in case p∗R= ˙p∗.58 The required reduction of ˙m and ˙m∗ to achieve full system stabilization is determined by